The generator matrix

 1  0  1  1  1 14  1  1 14  1  0  1  1  6  1  1  1  1  1  8  1 12  1  1 12  1  4  1  4 10  2  1  2  2  2  1
 0  1 11  6  5  1 11  0  1 14  1 13  6  1  8  3  5  1 10  1  6  1  3  9  1  8  1  9  1  1  2  7 14  6  0  0
 0  0 12  0  0  0  0  4  4  4  4  4  4  8  0  8 12  8  0  4  4  4  4  0  4 12  8 12  4  4 12 12 12  4  4  0
 0  0  0 12  0  4  4  4  8  8 12  8  4  8 12  0  4 12  8  0  4  4 12  8 12  0  4  4  0  4  0  0  8  4 12  0
 0  0  0  0  8  0  0  8  8  8  8  8  8  8  8  8  8  8  8  8  0  8  8  8  0  8  8  0  0  8  8  8  0  0  0  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  8  8  8  0  0  8  8  0  0  8  8  8  8  0  0  8  8  0  8  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  0  8  8  8  8  8  0  0  8  0  0  8  0  0

generates a code of length 36 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+46x^28+106x^29+241x^30+416x^31+1157x^32+1926x^33+3879x^34+5800x^35+5741x^36+5574x^37+3889x^38+2132x^39+1183x^40+314x^41+165x^42+96x^43+55x^44+16x^45+18x^46+4x^47+7x^48+2x^52

The gray image is a code over GF(2) with n=288, k=15 and d=112.
This code was found by Heurico 1.16 in 6.09 seconds.